Mayor Giuliani vowed yesterday to boot the Brooklyn Museum’s board of trustees if they open a controversial art exhibit next weekend – but museum officials said the show would go on.

“Since they seem to have no compunction about putting their hands in the taxpayers’ pockets” for the exhibit – which features a painting of the Virgin Mary splattered with elephant dung, and a dissected pig – “I’m not going to have any compunction about putting them out of business,” Giuliani said.

The latest threat came as other cultural institutions told legislative leaders they fear they’ll be next in line to have funding lopped off if the mayor doesn’t like a certain exhibit, and the art flap seemed headed for a First Amendment legal showdown.

“They are closing it down [to children under 17 years old] illegally under the lease,” Giuliani told reporters at a Harlem press conference – two days after he said he’ll pull the museum’s $7.2 million in city funds if it goes ahead with “Sensation: Young British Artists from the Saatchi Collection” next Saturday.

Giuliani, a Roman Catholic who slammed the show as “disgusting,” claims the lease prevents the museum from limiting access to any exhibit without his permission.

“The lease says that this board [of trustees] forfeits its right to run that museum, and the museum reverts to the city. And you can be darn sure that we will insist on those legal remedies,” the mayor said.

He blasted the exhibit as a “preserve for Catholic-bashers” that’s “purely and specifically for shock value in order to commercialize the museum.”

Museum spokeswoman Sally Williams said the exhibit will open next Saturday as planned, but said she couldn’t comment further.

New York Civil Liberties Union head Norman Siegel said his agency is ready to defend the museum in court.

Meanwhile, City Council Speaker Peter Vallone told the mayor he can’t support the eviction plan, even though he abhors the exhibit.

Vallone, a devout Catholic, said he’s gotten “several” calls from anxious officials at other cultural institutions.

“They’re concerned that this could set a precedent,” Vallone said. “I’ve assured them that as far as I know … we’re not going to set ourselves up as censors.”

Manhattan Borough President C. Virginia Fields also joined the flap, saying, “The mayor’s actions here open so many doors that we’ve been through before – the McCarthy era comes to mind immediately.”

Asked why he hasn’t tried to stop funding for other projects that go against Catholic values – like the New York Film Festival flick “Dogma,” featuring a descendant ofJesus working in an abortion clinic, which will be shown at Lincoln Center, Giuliani replied:

“I think all of these things have to be taken on an individual basis … In the case of the museum, there is a specific provision in the lease that gives me a legal remedy.”